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<div class="subTitle">org.apache.commons.math3.optimization.fitting</div>
<h2 title="Class HarmonicFitter.ParameterGuesser" class="title">Class HarmonicFitter.ParameterGuesser</h2>
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<pre>public static class <span class="strong">HarmonicFitter.ParameterGuesser</span>
extends <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre>
<div class="block">This class guesses harmonic coefficients from a sample.
 <p>The algorithm used to guess the coefficients is as follows:</p>

 <p>We know f (t) at some sampling points t<sub>i</sub> and want to find a,
 &omega; and &phi; such that f (t) = a cos (&omega; t + &phi;).
 </p>

 <p>From the analytical expression, we can compute two primitives :
 <pre>
     If2  (t) = &int; f<sup>2</sup>  = a<sup>2</sup> &times; [t + S (t)] / 2
     If'2 (t) = &int; f'<sup>2</sup> = a<sup>2</sup> &omega;<sup>2</sup> &times; [t - S (t)] / 2
     where S (t) = sin (2 (&omega; t + &phi;)) / (2 &omega;)
 </pre>
 </p>

 <p>We can remove S between these expressions :
 <pre>
     If'2 (t) = a<sup>2</sup> &omega;<sup>2</sup> t - &omega;<sup>2</sup> If2 (t)
 </pre>
 </p>

 <p>The preceding expression shows that If'2 (t) is a linear
 combination of both t and If2 (t): If'2 (t) = A &times; t + B &times; If2 (t)
 </p>

 <p>From the primitive, we can deduce the same form for definite
 integrals between t<sub>1</sub> and t<sub>i</sub> for each t<sub>i</sub> :
 <pre>
   If2 (t<sub>i</sub>) - If2 (t<sub>1</sub>) = A &times; (t<sub>i</sub> - t<sub>1</sub>) + B &times; (If2 (t<sub>i</sub>) - If2 (t<sub>1</sub>))
 </pre>
 </p>

 <p>We can find the coefficients A and B that best fit the sample
 to this linear expression by computing the definite integrals for
 each sample points.
 </p>

 <p>For a bilinear expression z (x<sub>i</sub>, y<sub>i</sub>) = A &times; x<sub>i</sub> + B &times; y<sub>i</sub>, the
 coefficients A and B that minimize a least square criterion
 &sum; (z<sub>i</sub> - z (x<sub>i</sub>, y<sub>i</sub>))<sup>2</sup> are given by these expressions:</p>
 <pre>

         &sum;y<sub>i</sub>y<sub>i</sub> &sum;x<sub>i</sub>z<sub>i</sub> - &sum;x<sub>i</sub>y<sub>i</sub> &sum;y<sub>i</sub>z<sub>i</sub>
     A = ------------------------
         &sum;x<sub>i</sub>x<sub>i</sub> &sum;y<sub>i</sub>y<sub>i</sub> - &sum;x<sub>i</sub>y<sub>i</sub> &sum;x<sub>i</sub>y<sub>i</sub>

         &sum;x<sub>i</sub>x<sub>i</sub> &sum;y<sub>i</sub>z<sub>i</sub> - &sum;x<sub>i</sub>y<sub>i</sub> &sum;x<sub>i</sub>z<sub>i</sub>
     B = ------------------------
         &sum;x<sub>i</sub>x<sub>i</sub> &sum;y<sub>i</sub>y<sub>i</sub> - &sum;x<sub>i</sub>y<sub>i</sub> &sum;x<sub>i</sub>y<sub>i</sub>
 </pre>
 </p>


 <p>In fact, we can assume both a and &omega; are positive and
 compute them directly, knowing that A = a<sup>2</sup> &omega;<sup>2</sup> and that
 B = - &omega;<sup>2</sup>. The complete algorithm is therefore:</p>
 <pre>

 for each t<sub>i</sub> from t<sub>1</sub> to t<sub>n-1</sub>, compute:
   f  (t<sub>i</sub>)
   f' (t<sub>i</sub>) = (f (t<sub>i+1</sub>) - f(t<sub>i-1</sub>)) / (t<sub>i+1</sub> - t<sub>i-1</sub>)
   x<sub>i</sub> = t<sub>i</sub> - t<sub>1</sub>
   y<sub>i</sub> = &int; f<sup>2</sup> from t<sub>1</sub> to t<sub>i</sub>
   z<sub>i</sub> = &int; f'<sup>2</sup> from t<sub>1</sub> to t<sub>i</sub>
   update the sums &sum;x<sub>i</sub>x<sub>i</sub>, &sum;y<sub>i</sub>y<sub>i</sub>, &sum;x<sub>i</sub>y<sub>i</sub>, &sum;x<sub>i</sub>z<sub>i</sub> and &sum;y<sub>i</sub>z<sub>i</sub>
 end for

            |--------------------------
         \  | &sum;y<sub>i</sub>y<sub>i</sub> &sum;x<sub>i</sub>z<sub>i</sub> - &sum;x<sub>i</sub>y<sub>i</sub> &sum;y<sub>i</sub>z<sub>i</sub>
 a     =  \ | ------------------------
           \| &sum;x<sub>i</sub>y<sub>i</sub> &sum;x<sub>i</sub>z<sub>i</sub> - &sum;x<sub>i</sub>x<sub>i</sub> &sum;y<sub>i</sub>z<sub>i</sub>


            |--------------------------
         \  | &sum;x<sub>i</sub>y<sub>i</sub> &sum;x<sub>i</sub>z<sub>i</sub> - &sum;x<sub>i</sub>x<sub>i</sub> &sum;y<sub>i</sub>z<sub>i</sub>
 &omega;     =  \ | ------------------------
           \| &sum;x<sub>i</sub>x<sub>i</sub> &sum;y<sub>i</sub>y<sub>i</sub> - &sum;x<sub>i</sub>y<sub>i</sub> &sum;x<sub>i</sub>y<sub>i</sub>

 </pre>
 </p>

 <p>Once we know &omega;, we can compute:
 <pre>
    fc = &omega; f (t) cos (&omega; t) - f' (t) sin (&omega; t)
    fs = &omega; f (t) sin (&omega; t) + f' (t) cos (&omega; t)
 </pre>
 </p>

 <p>It appears that <code>fc = a &omega; cos (&phi;)</code> and
 <code>fs = -a &omega; sin (&phi;)</code>, so we can use these
 expressions to compute &phi;. The best estimate over the sample is
 given by averaging these expressions.
 </p>

 <p>Since integrals and means are involved in the preceding
 estimations, these operations run in O(n) time, where n is the
 number of measurements.</p></div>
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<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/optimization/fitting/HarmonicFitter.ParameterGuesser.html#HarmonicFitter.ParameterGuesser(org.apache.commons.math3.optimization.fitting.WeightedObservedPoint[])">HarmonicFitter.ParameterGuesser</a></strong>(<a href="../../../../../../org/apache/commons/math3/optimization/fitting/WeightedObservedPoint.html" title="class in org.apache.commons.math3.optimization.fitting">WeightedObservedPoint</a>[]&nbsp;observations)</code>
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<td class="colFirst"><code>double[]</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/optimization/fitting/HarmonicFitter.ParameterGuesser.html#guess()">guess</a></strong>()</code>
<div class="block">Gets an estimation of the parameters.</div>
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<h4>HarmonicFitter.ParameterGuesser</h4>
<pre>public&nbsp;HarmonicFitter.ParameterGuesser(<a href="../../../../../../org/apache/commons/math3/optimization/fitting/WeightedObservedPoint.html" title="class in org.apache.commons.math3.optimization.fitting">WeightedObservedPoint</a>[]&nbsp;observations)</pre>
<div class="block">Simple constructor.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>observations</code> - Sampled observations.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a></code> - if the sample is too short.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/ZeroException.html" title="class in org.apache.commons.math3.exception">ZeroException</a></code> - if the abscissa range is zero.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/MathIllegalStateException.html" title="class in org.apache.commons.math3.exception">MathIllegalStateException</a></code> - when the guessing procedure cannot
 produce sensible results.</dd></dl>
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<h4>guess</h4>
<pre>public&nbsp;double[]&nbsp;guess()</pre>
<div class="block">Gets an estimation of the parameters.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the guessed parameters, in the following order:
 <ul>
  <li>Amplitude</li>
  <li>Angular frequency</li>
  <li>Phase</li>
 </ul></dd></dl>
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